Unsupportable Finite Cells

An unexpected discovery I made while writing
Great Stella,
is that some finite cells for some Archimedean stellations, can't be fully
supported by other finite cells. In other words, they are partly supported by
infinite cells. Infinite cells which have some finite faces pointing away from
the centre of the model. It's hard to explain, but it's very surprising for
anyone who knows what I'm talking about.

Another way of saying this is that the final stellation is re-entrant.
Here, the final stellation is the one consisting of all finite stellation
cells, and re-entrant means not fully supported. Fully supported means that
any ray from the centre of the model out to infinite will only cross the
model's surface once.

This situation arises for the following Archimedean/dual models:

Snub Cube.

Snub dodecahedron.

Pentagonal hexecontahedron.

It also happens for various non-convex uniform solids. Interesting that it
happens for the snub dodecahedron and its dual, but the snub cube's dual is not
included in the list.

If you want to see what those unusual cells look like, you can use the
"Stellation>Fill All Unsupportable Cells" menu item in
Great Stella,
which will only have an effect for the few models that demonstrate this weird
behaviour.